On the class of Banach spaces with James constant √2, III

A New Class of Banach Sequence Spaces

An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure

We create a new family of Banach spaces, the James–Schreier spaces, by amalgamating two important classical Banach spaces: James’ quasi-reflexive Banach space on the one hand and Schreier’s Banach space giving a counterexample to the Banach–Saks property on the other. We then investigate the properties of these James–Schreier spaces, paying particular attention to how key properties of their ‘a...

The retraction constant in some Banach spaces

We give new sharper estimations for the retraction constant in some Banach spaces. r 2002 Elsevier Science (USA). All rights reserved.

On the James Type Constant and Von Neumann–jordan Constant for a Class of Banaś–fra̧czieck Type Spaces

As a generalization of Banaś-Fra̧czieck space, the space Xλ ,p that denotes R 2 endowed with the norm ‖x‖λ ,p = max{λ |x1 |,‖x‖p} for λ > 1 , p 1 and x = (x1,x2) ∈ R2 is well defined. In this note, the exact value of the the James type constants JXλ ,p ,t(1) and von Neumann-Jordan constant CNJ (Xλ ,p) about this space for p 2 are investigated.

A Class of Hereditarily $ell_p(c_0)$ Banach spaces

We extend the class of Banach sequence spaces constructed by Ledari, as presented in ''A class of hereditarily $ell_1$ Banach spaces without Schur property'' and obtain a new class of hereditarily $ell_p(c_0)$ Banach spaces for $1leq p<infty$. Some other properties of this spaces are studied.